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Not sure about total levels/flagship but ASW does seem to have some factor on A-3.
For the runs I did today this one ended up succeeding:
This one is that last one I managed to do before bed and it failed:

Total ASW: 245 - 4 ships with a total of 3 SONAR, 4 depth charges among them
LoS: 12.13

This almost same fleet failed with the lower level cl..and to make it 'valid comparison', made sure the gear was swapped between the CL but no other changes

EDIT: looking at your two runs @chronomeister, and then comparing mine.. wonder if it isn't so much "You must have over x ASW" but more "You must have 2+ SONAR"...akin to drums/overdrumming. In both your runs your levels were higher and your ASW higher..but the difference is I used more SONAR.

So something for a requirement of "1 CL, 4 DD/DE, flag over 50, [fleet over x?], must have 2 SONAR (on two ships?) [more sonar = better chance of great success]" Like a variant of Expeditions 21/37/38

I used a normal expedition fleet for A1/A2/A3, and worked just fine (Kinu as flagship, Shiratsuyu, Murasame, Harusame, Kawakaze, Kamikaze - all with daihatsu or drums). Granted, the lowest level was 71.

So it is confirmed that AA and LOS affects the success rate as well. The two groups both have 180 asw and same lv, but different aa and los. The first two fleet fail in A2, but the next 2 groups with higher aa and los success.